Apparatus for online signature verification using pattern transform technique and method therefor

ABSTRACT

In an apparatus for online signature verification, a signature data input unit digitalizes a locus of a user signature and reads the locus as a sequence of points. A first and a second pattern transform unit performs a speed equalization and a velocity transform on the signature sequence and generates a first and a second transformed pattern sequence, respectively. A characteristics extraction unit extracts three characteristics vectors from the signature sequence, the first and the second transformed pattern sequence, respectively, to thereby generate the three characteristics vectors. A difference vector estimation unit generates a difference vector. A determination unit determines whether an input signature and the reference signature are signed by a single person.

CROSS REFERENCE TO RELATED APPLICATION

This application is the National Phase application of InternationalApplication No. PCT/KR2003/000523, filed Mar. 18, 2003, which designatesthe United States and was published in English. This application, in itsentirety, is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to a user verification technique based onbiological characteristics; and, more particularly, to an apparatus foronline signature verification using a pattern transform technique and amethod therefor, which is suitable for visualizing dynamiccharacteristics of an online signature pattern such as a signatureinputted by a tablet digitizer and improving a performance of analyzingon the dynamic characteristics of a signing process by using thevisualized pattern.

BACKGROUND OF THE INVENTION

An identification of a person has required checking information, e.g., apassword, and identification tools such as a key and a card. However,there is a drawback in that a user may forget the password or theidentification tools may be lost or stolen. To that end, a great deal ofresearch has been devoted to development of a biometric verificationmethod for identifying a person based on his unique biometriccharacteristics.

Especially, a signature verification method is a representative exampleusing behavioral biometric characteristics detected from a personalsignature. The method is considered to have a lower accuracy incomparison with a method using other biometric characteristics, e.g.,fingerprints. However, the method is culturally and socially acceptableand users may easily adapt themselves thereto, so that it is regarded asa useful method.

Since a signature is a pattern based on each person's name, everysignature is different in its pattern, and therefore, one can be easilydistinguished from another. However, in case similar patterns areintentionally generated (these patterns are called skilled forgery), thepatterns are hardly distinguishable. Accordingly, it is required todistinguish the skilled forgery from a genuine signature.

When a signature is forged, a forger makes an effort to imitate anoriginal pattern. Thus, it takes much longer to sign or a signingbecomes slower at a certain point. These dynamic characteristics of asigning process are hardly forgeable and therefore are considered to beimportant information for distinguishing the skilled forgery from theoriginal pattern.

Signature information captured by using a tablet digitizer includesinformation on a signature pattern and the dynamic characteristics ofthe signing process. However, information on the dynamic characteristicsare not reflected to a completed signature pattern but available only inthe form of additional information, so that the information thereon arehardly recognized by a pattern analysis method used for generalsignature recognition.

In order to solve such problem, the dynamic characteristics have beenconventionally represented as simplified parameters such as a totalsigning time, an average velocity and an average acceleration.

However, a conventional method using the dynamic characteristicsrepresented as the simplified parameters has disadvantages in that aconsiderable amount of information may be lost, which in turn causesdeterioration of a distinction between signatures, i.e., genuine vs.forgery. As a result, a more efficient method for analyzing dynamiccharacteristics is required.

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to provide anapparatus for online signature verification using a pattern transformtechnique and a method therefor, which securely verifies an identity ofa signer and improves a distinction between a skilled forgery and anoriginal signature by analyzing characteristics of a transformedpattern, i.e., visualized dynamic characteristics of a signature patternthrough a speed equalization and a velocity transform technique.

In accordance with one aspect of the invention, there is provided anapparatus for online signature verification analyzing a referencesignature database (DB) of a specific user, the apparatus including: asignature data input unit for capturing a locus of a user signature andreading the digitized locus as a sequence of points sampled at regulartime intervals; a first pattern transform unit for performing a speedequalization on the signature sequence read by the signature data inputunit and generating a first transformed pattern sequence; a secondpattern transform unit for performing a velocity transform on thesignature sequence read by the signature data input unit and generatinga second transformed pattern sequence; a feature extraction unit forextracting three feature vectors from, the signature sequence read bythe signature data input unit, the first pattern sequence transformed bythe first pattern transform unit and the second pattern sequencetransformed by the second pattern transform unit, respectively, tothereby generate the three feature vectors having different information;a difference vector estimation unit for generating a difference vectorbetween the feature vector of the specific user's reference signatureread from the reference DB and the feature vector extracted by thefeature extraction unit; and a determination unit for determiningwhether an input signature and the reference signature are signed by asingle person, based on the difference vector generated from thedifference vector estimation unit.

In accordance with another aspect of the invention, there is provided amethod for online signature verification analyzing a reference signatureDB of a specific user, the method including the steps of: (a) capturinga locus of a user signature and reading the digitized locus as asequence of points sampled at regular time intervals; (b) performing aspeed equalization on the signature sequence read in the step (a) togenerate a first transformed pattern sequence; (c) performing a velocitytransform on the signature sequence read in the step (a) to generate asecond transformed pattern sequence; (d) extracting three featurevectors from the signature sequence read in the step (a), the firstpattern sequence transformed in the step (b) and the second patternsequence transformed in the step (c), respectively, to thereby generatethree feature vectors having different information; (e) generating adifference vector between the feature vector of the specific user'sreference signature read from the reference signature DB and the featurevector extracted in the step (d); and (f) determining whether an inputsignature and the reference signature are signed by a single person,based on the difference vector generated in the step (e).

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and features of the present invention willbecome apparent from the following description of preferred embodiments,given in conjunction with the accompanying drawings, in which:

FIG. 1 shows a block diagram for illustrating an apparatus for onlinesignature verification using a pattern transform technique in accordancewith a preferred embodiment of the present invention;

FIGS. 2A and 2B illustrate an example of a signature pattern and itsspeed-equalized pattern in accordance with the present invention,respectively;

FIGS. 3A and 3B describe an example of a skilled forgery and itsspeed-equalized pattern in accordance with the present invention,respectively;

FIGS. 4A and 4B offer examples of velocity-transformed signaturepatterns in accordance with the present invention;

FIG. 5 provides a radial histogram for illustrating radially divided 16bins; and

FIG. 6 presents a detailed diagram for showing a determination unit ofFIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, a preferred embodiment of the present invention will bedescribed in detail with reference to the accompanying drawings.

FIG. 1 shows a block diagram for illustrating an apparatus for onlinesignature verification using a pattern transform technique in accordancewith a preferred embodiment of the present invention, wherein theapparatus includes a signature data input unit 100, transform units 101and 102, a feature extraction unit 104, a reference signature database106, a difference vector estimation unit 108 and a determination unit110.

As illustrated in FIG. 1, the signature data input unit 100 digitizes alocus of a user signature and the digitalized locus of the usersignature is read as a sequence of points sampled at regular timeintervals.

The signature sequence C read by the signature data input unit 100 isrepresented as a two-dimensional vector list C={p₁, p₂, . . . , p_(N)},and each of the points is sampled at the regular time intervals, whereina property of each point p_(i), i.e., x-coordinate and y-coordinate areindicated as p_(i)(x) and p_(i)(y), respectively.

The transform unit 101 and 102 respectively perform a speed equalizationand a velocity transform in accordance with the present invention on thesignature sequence C read by the signature data input unit 100 togenerate respective transformed patterns.

A first transform unit 101 is a speed equalization transform unit forrecomposing a signature pattern on the assumption that linear velocitieson the locus of the signature pattern are regular. After a transform isperformed, a length of a section where a signer quickly signs becomesshorter, while a length of a section where the signer slowly signedbecomes longer in comparison with other sections.

The transformed results affect a pattern by visualizing dynamiccharacteristics of a signing process and become a basis for analyzingthe dynamic characteristics.

Specifically, an input signature pattern C={p₁, p₂, . . . , p_(N)} istransformed into another two-dimensional vector list S={s₁, s₂, . . . ,s_(N)}.

The first horizontal and vertical derivative v_(x) and v_(y) on eachpoint p_(i) of the locus are obtained as follows:v _(x)=(−p _(i+2)(x)+8·p _(i+1)(x)−8·p _(i−1)(x)+p _(i−2)(x))/12v _(y)=(−p _(i+2)(y)+8·p _(i+1)(y)−8p _(i−1)(y)+p _(i−2)(y))/12  Eq. (1)

Based on a result of Eq. (1), a direction of the locus on the pointp_(i) is searched as follows:

$\begin{matrix}{\theta = {{arc}\;{\tan\left( \frac{v_{y}}{v_{x}} \right)}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$

An element s_(i) of the two-dimensional vector list S, which istransformed by using Eq. (1) and Eq. (2), is calculated as follows:s _(i) =p _(i) i=1, 2s _(i) =s _(i−1)+(p _(i) −p _(i−1)) i=N−1, Ns _(i) =s _(i−1) +vΔt·Θ otherwise  Eq. (3)

In Eq. (3), v is a constant designating the velocity and Δt is aconstant designating the time interval between sampling points, whichmeans sampling is performed at regular intervals.

Meanwhile, Θ represents a unit vector in the direction of θ, i.e., thelocus direction on the point p_(i) obtained by Eq. (2). A locus of atransformed pattern has the same direction as that of an originalpattern. However, since the velocity is a constant, a length of thelocus becomes in proportion to a time taken to draw the locus.Therefore, the transformed pattern becomes significantly different fromthe original pattern.

FIGS. 2A and 2B illustrate drawings for comparing an original patternwith a speed-equalized pattern.

Referring to FIGS. 3A and 3B, there are illustrated a skilled forgery ofa signature shown in FIG. 2A and a speed-equalized pattern thereof.

As can be seen from FIGS. 2A and 3A, the patterns in FIGS. 2A and 3A arequite similar. On the other hand, the transformed patterns in FIGS. 2Band 3B are significantly different. In other words, an originalsignature and a skilled forgery have similar patterns, but dynamiccharacteristics thereof are significantly different. Thus, the skilledforgery can be effectively distinguished from the original signature bymaking a comparison in transformed domain.

A second transform unit 102 of FIG. 1 is a velocity transform device fortransforming a spatial pattern into a velocity domain. Specifically, aninput signature pattern C={p₁, p₂, . . . , p_(N)}, is transformed intoanother two-dimensional vector list V={v₁, v₂, . . . , v_(N)} by usingEq. (4) as follows:v _(i) =v ₃ i=1, 2v _(i) =v _(N−2) i=N−1, Nv _(i)=(v _(xi) , v _(yi)) otherwise  Eq. (4)

The value of v₃ is assigned to v₁ and v₂, and the value of v_(N−2) isassigned to v_(N−1) and V_(N). Values of the rest of points aredetermined by calculating v_(xi) and v_(yi). The v_(xi) and v_(yi) inEq. (4) represent the first horizontal and vertical derivative on thepoint p_(i), respectively, which are obtained by using Eq. (1).

FIGS. 4A and 4B provide transformed results of FIGS. 2A and 3A by aspeed transform technique.

While original patterns are quite similar, transformed patterns thereofare considerably different. Therefore, when signature verification isperformed in a transformed domain, it is possible to effectively discerna skilled forgery from an original signature.

When transform methods in accordance with the present invention, i.e., aspeed equalization and a velocity transform technique, are used, atransformed pattern is represented in the same format as an originalpattern. That is to say, every type of signature verification methodsthat have been developed for online signature verification can be alsoapplied to a transformed pattern. As a result, conventional signatureverification methods can consider information on dynamiccharacteristics, to thereby enable a skilled forgery to be moreeffectively distinguished from an original signature.

Accordingly, the transform methods of the present invention are notconfined to characteristics vector typed signature verification to bedescribed later, but applicable to every online signature verificationmethod for signature patterns.

Referring back to FIG. 1, the feature extraction unit 104 extracts afeature vector representing characteristics of each pattern from aninput signature pattern and transformed patterns thereof, wherein thefeature vector is a set of parameters indicating characteristics of asignature pattern. In this case, the apparatus for signatureverification of the present invention uses parameters shown in followingTable 1.

TABLE 1 Total Signing Time total time taken for signing Pen DownDuration duration of contact between a pen and a tablet Number of PenUpsthe number of lifting a pen during a signing process Positive v_(x)duration duration of horizontal velocity having a positive valueNegative v_(x) duration duration of horizontal velocity having anegative value Positive v_(y) duration duration of vertical velocityhaving a positive value Negative v_(y) duration duration of verticalvelocity having a negative value x velocity average horizontal velocityy velocity average vertical velocity Aspect Ratio a ratio of height towidth Upper to Lower Ratio a ratio of number of sample points above acenter of gravity to number of sample points below the center of gravityLeft to Right Ratio a ratio of number of sample points to the left of acenter of gravity to number of sample points to the right of center ofgravity Center Cross number of crossing between a signature locus and ahorizontal line passing a center of gravity IM1 Invariant Moment #1 IM2Invariant Moment #2 IM3 Invariant Moment #3 IM4 Invariant Moment #4 IM5Invariant Moment #5 IM6 Invariant Moment #6 IM7 Invariant Moment #7Direction Histogram histogram of the direction at each point (the numberof bins = 8) Radial Histogram radial distribution histogram of samplepoints (the number of bins = 16)

In comparison with a conventional apparatus, the apparatus for signatureverification of the present invention has an advantage in that anaccuracy of verification can be greatly improved by using a featurevector integrated with three pairs of parameters having differentinformation, wherein the characteristics vector is not only obtainedfrom an input signature pattern but also extracted from a speedequalized pattern and a velocity transformed pattern.

Since most coefficients mentioned in Table 1 are described in otherdocuments, a specific explanation thereof is omitted. Instead, a radialhistogram, which is a feature of the present invention, will bedescribed briefly.

The radial histogram illustrates a distribution of sample points inradially divided 16 bins as shown in FIG. 5 on a Cartesian coordinatesystem of which the origin is the center of gravity of a pattern,wherein the distribution is based on locations where a signature locuspasses.

The difference vector estimation unit 108 generates a difference vectorbetween a characteristics vector of a reference signature and acharacteristics vector extracted from an input signature.

Each element of the difference vector has an absolute value of adifference between each element of the characteristics vectors as shownin Eq. (5) as follows:F _(Di) =|F _(Ti) −F _(Ei)|  Eq. (5)wherein F_(Di), F_(Ti), and F_(Ei) indicate I^(th) element of thedifference vector, the characteristics vector of the input signature andthe characteristics vector of the reference signature, respectively.

However, each element of the direction histogram and the radialhistogram in the parameter list of Table 1 is interdependent each other,and therefore, a sum of differences instead of each of the differencesis inserted in the difference vector as shown in Eq. (6) as follows:

$\begin{matrix}{D = {\sum\limits_{i = 1}^{N}{{{H_{r}(i)} - {H_{t}(i)}}}}} & {{Eq}.\mspace{14mu}(6)}\end{matrix}$wherein the D, N and H(i) represent a difference between the histograms,number of bins and a histogram value of an I^(th) bin, respectively.Further, the subscripts r and t indicate a reference and a test pattern,respectively.

The original characteristics vector has 44 elements as shown in Table 1,but the difference vector has 22 elements, since the direction histogramand the radial histogram are represented by a single value,respectively.

The determination unit 110 determines whether or not an input signatureand a reference signature are signed by the same person, based on thedifference vector calculated in the difference vector estimation unit108. Further, the determination unit 110 uses an artificial neuralnetwork integrated with three layers, i.e., an input layer, a hiddenlayer and an output layer having two neurons, as illustrated in FIG. 6to determine whether or not the input signature and the referencesignature are signed by the same person.

In this case, the three pairs of characteristics vectors of Table 1 arerespectively extracted from an original pattern and transformedpatterns. A vector integrated with the three pairs thereof is inputtedinto an input parts (F₁−F_(N)) of the artificial neural network. The twoneurons of the output layer are trained to output 1 and 0 for identicalsignatures but 0 and 1 for different signatures. Therefore, thedetermination unit 110 uses the difference between the two values (thedifference has a value between −1 and 1 and increases in proportion tothe similarity of the signatures) to determine whether the signature isan original or a forgery. To be specific, the signature is determined tohave been signed by the same person if the difference is larger than athreshold. On the other hand, the signature is determined to be askilled forgery if the difference is smaller than the threshold.

As described above, an online signature verification technique using atransform method in accordance with the present invention generates apattern to which dynamic characteristics of a signing process arereflected through a transform technique, so that an analysis of thedynamic characteristics can be performed effectively. Accordingly, askilled forgery, which is hardly distinguishable by using only staticcharacteristics, can be accurately distinguished in accordance with thepresent invention, thereby greatly improving a performance of userverification.

While the invention has been shown and described with respect to thepreferred embodiments, it will be understood by those skilled in the artthat various changes and modifications may be made without departingfrom the spirit and scope of the invention as defined in the followingclaims.

1. An apparatus for online signature verification using a referencesignature database (DB), the apparatus comprising: a signature datainput unit for digitalizing a locus of a user's input signature andreading the digitized locus as a signature sequence of sample pointssampled at regular time intervals; a first pattern transform unit forperforming a speed equalization on the signature sequence read by thesignature data input unit and generating a first transformed patternsequence, wherein said speed equalization is based on the assumptionthat linear velocities at the sample points on the locus are equal to aconstant value; a second pattern transform unit for performing avelocity transformation on the signature sequence read by the signaturedata input unit and generating a second transformed pattern sequence; afeature extraction unit for extracting a characteristics vector from thesignature sequence, the first transformed pattern sequence and thesecond transformed pattern sequence; a difference vector estimation unitfor generating a difference vector between a feature vector of theuser's reference signature read from the reference signature DB and thecharacteristics vector extracted by the feature extraction unit; and adetermination unit for determining whether the input signature and thereference signature are signed by the same person or not, based on thedifference vector generated from the difference vector estimation unit.2. The apparatus of claim 1, wherein the speed equalization is performedby using the following equation:s _(i) =p _(i) i=1, 2s _(i) =s _(i−1)+(p _(i) −p _(i−1)) i=N−1, Ns _(i) =s _(i−1) +vΔt·Θ otherwise wherein p_(i) represents the i^(th)sample point on the signature sequence of the digitized locus, s_(i)represents the corresponding i^(th) element of the first transformedpattern sequence, v represents the constant velocity, Δt represents thesampling time interval between the sample points on the signaturesequence, and Θ represents a unit vector in the direction θ of th edigitized locus at the sample point p_(i).
 3. The apparatus of claim 1,wherein the velocity transformation is performed by using the followingequation:v _(i) =v ₃ i=1, 2v _(i) =v _(N−2) i=N−1, Nv _(i)=(v _(xi) , v _(yi)) otherwise wherein v_(i) is the i^(th) elementof the second transformed pattern sequence and v_(xi) and v_(yi) arefirst horizontal and vertical derivatives at the corresponding samplepoint p_(i) on the digitized locus.
 4. The apparatus of claim 1, whereinthe speed equalization is a technique for recomposing a signaturepattern based on an inverse proportional relation between a signaturespeed and a length of the pattern, and the velocity transformation is atechnique for transforming a spatial pattern into a velocity domain. 5.An online signature verification method using a reference signature DB,the method comprising the steps of: (a) digitalizing a locus of a user'sinput signature and reading the digitized locus as a signature sequenceof sample points sampled at regular time intervals; (b) performing aspeed equalization on the signature sequence read in the step (a) togenerate a first transformed pattern sequence, wherein said speedequalization is based on the assumption that linear velocities at thesample points on the locus are equal to a constant value; (c) performinga velocity transformation on the signature sequence read in the step (a)to generate a second transformed pattern sequence; (d) extracting acharacteristics vector from the signature sequence read in the step (a),the first transformed pattern sequence generated in the step (b) and thesecond transformed pattern sequence generated in the step (c); (e)generating, a difference vector between a feature vector of the user'sreference signature read from the reference signature DB and thecharacteristics vector extracted in the step (d); and (f) determiningwhether the input signature and the reference signature are signed bythe same person or not, based on the difference vector generated in thestep (e).
 6. The method of claim 5, wherein the speed equalization isperformed by using the following equation:s _(i) =p _(i) i=1,2s _(i) =s ¹⁻¹+(p _(i) −p _(i−1)) i=N−1, Ns _(i) =s _(i−1) +vΔt•Θotherwise wherein p_(i) represents the i^(th)sample point on the signature sequence of the digitized locus, s_(i)represents the corresponding i^(th) element of the first transformedpattern sequence, v represents the constant velocity, Δt represents thesampling time interval between the sample points on the signaturesequence, and Θ represents a unit vector in the direction 0 of thedigitized locus at the sample point p_(i).
 7. The method of claim 5,wherein the velocity transformation is performed by using the followingequation:v _(i) =v ₃ i=1,2v _(i) =v _(N−2) i=N−1, Nv _(i)=(v _(xi), v_(yi)) otherwise wherein v_(i) is the i^(th) elementof the second transformed pattern sequence, and v_(xi) and v_(yi) arefirst horizontal and vertical derivatives at the corresponding samplepoint p_(i) on the digitized locus.
 8. The method of claim 5, whereinthe speed equalization is a technique for recomposing a signaturepattern based on an inverse proportional relation between a signaturespeed and a length of the pattern, and the velocity transformation is atechnique for transforming a spatial pattern into a velocity domain. 9.The method of claim 6, wherein the direction θ of the digitized locus atthe sample point p_(i) is determined by the following equation:θ=arctan(v _(yi) /v _(xi)) wherein v_(xi) and v_(y i) are firsthorizontal and vertical derivatives at the sample point p_(i).
 10. Themethod of claim 9, wherein the velocity transformation is performed byusing the following equation:v _(i) =v ₃ i=1,2v _(i) =v _(N−2) i=N−1, Nv _(i)=(v _(xi) , v _(yi)) otherwise wherein v_(i) is the i^(th) elementof the second transformed pattern sequence.
 11. The method of claim 10,wherein the first horizontal and vertical derivatives at the samplepoint p, are determined by the following equations:v _(xi)=(−p _(i+2)(x)+8 p _(i+1)(x)−8 p _(i−1)(x)+p _(i−2)(x))/12v _(yi)=(−p _(i+2)(y)+8 p _(i+1)(y)−8 p _(i−1)(y)+p _(i−2)(y))/12. 12.The method of claim 5, wherein the sample points are distributedaccording to a radial histogram which comprises bins successivelyarranged around the origin of a Cartesian coordinate system, and whereinthe distribution is based on locations where the locus passes.
 13. Theapparatus of claim 2, wherein the direction θ of the digitized locus atthe sample point p_(i) is determined by the following equation:θ=arctan(v _(yi) /v _(xi)) wherein v_(xi) and v_(yi) are firsthorizontal and vertical derivatives at the sample point p_(i).
 14. Theapparatus of claim 13, wherein the velocity transformation is performedby using the following equation:v _(i) =v ₃ i=1,2v _(i) =v _(N−2) i=N−1, Nv _(i)=(v _(xi), v_(yi)) otherwise wherein v_(i) is the i^(th) elementof the second transformed pattern sequence.
 15. The apparatus of claim14, wherein the first horizontal and vertical derivatives at the samplepoint p_(i) are determined by the following equations:v _(xi)=(−p _(i+2)(x)+8 p _(i+1)(x)−8 p _(i−1)(x)+p _(i−2)(x))/12v _(yi)=(−p _(i+2)(y)+8 p _(i+1)(y)−8 p _(i−1)(y)+p _(i−2)(y))/12. 16.The apparatus of claim 1, wherein the sample points are distributedaccording to a radial histogram which comprises bins successivelyarranged around the origin of a Cartesian coordinate system, and whereinthe distribution is based on locations where the locus passes.